More details on Spring design are to be found in the links below
the table.

Introduction

Leaf Springs are widely used in the automobile and railway industries
for suspension applications. The simplest variation is the single beam
spring. The more normal application is the laminated (multiple)
leaf spring which provides a more efficient stress distribution..

Single Leaf Springs have the following characteristics.

They are suitable for low and medium load forces

They have reasonably linear working characteristics

They have relatively low spring constant

They are long items with relatively low cross section

They are relatively low cost items

Laminated leaf springs have the following characteristics

They are suitable for higher loading forces

They have theoretically linear working characteristics (friction between the leaves causes hysteretic pattern of the working curve)

Compared to single leaf springs they have relatively high spring constants (stiffness)

Laminated spings have high space requirements compared to single leaf springs

There are two primary variations the cantilever spring and the simply supported beam..

Cantilever spring

Simply supported spring

Multiple leaf springs

Considering a cantilever type leaf spring, the stress distribution is related to the
distance from the load point.

σ = 6Fx / bt2

If (x/b) is constant along beam, of constant thickness t, then the stress level will
be constant and the most efficient spring will result. If x/b is constant
then a triangular shaped spring results. The multileaf spring is designed to provide a constant stress level along
the spring length as it is designed to be equivalent to a triangular spring as shown below.

For this spring the maximum stress( which ideally is constant along the spring) is
and the stiffness are as follows..

These equations apply to the quarter elliptic spring as shown below

The relevant equations for the semi-elliptic spring as shown below are